Off-cut Recycle in Multicomponent Separation

This section presents the dynamic optimisation problem formulation of Mujtaba (1989) and Mujtaba and Macchietto (1992) to obtain optimal recycle policies in multicomponent batch distillation. Some special cases were identified where the methods used for the binary case could be applied fairly easily to multicomponent mixtures. The previously mentioned measure q of the degree of difficulty of separation was used to identify those special cases. A new operational strategy regarding the order of off-cuts recycle in a multicomponent environment was discussed. The Benefits of recycling were correlated against the measure q. 

Dls is the solution of Equations 8.1-8.4 given Bs0, x Du and x B2 tnr is the batch time without recycle using 5 kmol (fixed reboiler charge) of fresh feed for the given separation x DI and x B2 (this time is same as those reported in Table 8.1 as tnr) 

Pnr = Productivity without recycle = BC / tnn kmol/hr Pr = Productivity with recycle = Bs0 / trS, kmol/hr X=% Productivity increase = (Pr - Pnr) xlOO I Pnr Note In all cases xB0, Vc and xR1 are the same as those used in Table 8.1 

As discussed in the previous section, the work of Mayur et al. (1970) and Christensen and Jorgensen (1987) on the optimal recycle policy was restricted to binary mixtures. The benefits of recycling were measured in terms of a reduction in batch time although increase in productivity could be a possible alternative. Luyben (1988) considered this productivity measure (as defined as capacity which includes both batch time and a constant charging and cleaning time) in a simulation of multicomponent batch distillation with recycle. Luyben (1988), however, showed the effect of different parameters (no of plates, relative volatilities, etc.) on the productivity and did not actually consider the effect of off-cuts recycle on the productivity. 

The mathematical formulation of the dynamic optimisation problem to obtain optimal off-cut recycle policy was done for a quasi-steady state operation using binary mixtures where there was only one main-cut and one off-cut (Mayur et al., 

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